Vibrations of linear piezostructures / Andrew J Kurdila and Pablo A. Tarazaga.

Format:

Book

Author/Creator:

Kurdila, Andrew, author.

Tarazaga, Pablo (Pablo A.), author.

Series:

Wiley-ASME Press

Language:

English

Subjects (All):

Piezoelectricity.

Physical Description:

1 online resource (259 pages)

Place of Publication:

Hoboken, New Jersey : Wiley, [2021]

Summary:

"Vibrations of Linear Piezostructures is a self-contained and introductory text providing a focused and concise account of the general theory of vibrations of linear piezostructures. While piezoelectric materials and sensors have been studied for decades, a person seeking a general introduction to the theory for modeling and analysis of this emerging class of sensors, actuators, and active systems currently must assimilate approaches from older outdated texts, journal or conference articles, edited volumes, highly specialized texts, or manuscripts that primarily treat other topics such as crystallography, tensor mathematics, continuum mechanics, or continuum electrodynamics. The book deals with the fundamental principals, starting with a review of mathematics, continuum mechanics and elasticity, and continuum electrodynamics as they are applied to electromechanical piezostructures. It continues by developing the work related to linear constitutive laws of piezoelectricity. Following this, it addresses modeling of linear piezostructures via Newton's approach and consequently via Variational Methods. And in the end it presents a general discussion of weak and strong forms of the equations of motion, Galerkin approximation methods for the weak form, Fouier or modal methods, and finite element methods."-- Provided by publisher.

Contents:

Cover

Title Page

Copyright

Contents

Foreword

Preface

Acknowledgments

List of Symbols

Chapter 1 Introduction

1.1 The Piezoelectric Effect

1.1.1 Ferroelectric Piezoelectrics

1.1.2 One Dimensional Direct and Converse Piezoelectric Effect

1.2 Applications

1.2.1 Energy Applications

1.2.2 Sensors

1.2.3 Actuators or Motors

1.3 Outline of the Book

Chapter 2 Mathematical Background

2.1 Vectors, Bases, and Frames

2.2 Tensors

2.3 Symmetry, Crystals, and Tensor Invariance

2.3.1 Geometry of Crystals

2.3.2 Symmetry of Tensors

2.4 Problems

Chapter 3 Review of Continuum Mechanics

3.1 Stress

3.1.1 The Stress Tensor

3.1.2 Cauchy's Formula

3.1.3 The Equations of Equilibrium

3.2 Displacement and Strain

3.3 Strain Energy

3.4 Constitutive Laws for Linear Elastic Materials

3.4.1 Triclinic Materials

3.4.2 Monoclinic Materials

3.4.3 Orthotropic Materials

3.4.4 Transversely Isotropic Materials

3.5 The Initial‐Boundary Value Problem of Linear Elasticity

3.6 Problems

Chapter 4 Review of Continuum Electrodynamics

4.1 Charge and Current

4.2 The Electric and Magnetic Fields

4.2.1 The Definition of the Static Electric Field

4.2.2 The Definition of the Static Magnetic Field

4.3 Maxwell's Equations

4.3.1 Polarization and Electric Displacement

4.3.2 Magnetization and Magnetic Field Intensity

4.3.3 Maxwell's Equations in Gaussian Units

4.3.4 Scalar and Vector Potentials

4.4 Problems

Chapter 5 Linear Piezoelectricity

5.1 Constitutive Laws of Linear Piezoelectricity

5.2 The Initial‐Value Boundary Problem of Linear Piezoelectricity

5.2.1 Piezoelectricity and Maxwell's Equations

5.2.2 The Initial‐Boundary Value Problem

5.3 Thermodynamics of Constitutive Laws

5.4 Symmetry of Constitutive Laws for Linear Piezoelectricity.

5.4.1 Monoclinic C2 Crystals

5.4.2 Monoclinic Cs Crystals

5.4.3 Trigonal D3 Crystals

5.4.4 Hexagonal C6v Crystals

5.5 Problems

Chapter 6 Newton's Method for Piezoelectric Systems

6.1 An Axial Actuator Model

6.2 An Axial, Linear Potential, Actuator Model

6.3 A Linear Potential, Beam Actuator

6.4 Composite Plate Bending

6.5 Problems

Chapter 7 Variational Methods

7.1 A Review of Variational Calculus

7.2 Hamilton's Principle

7.2.1 Uniaxial Rod

7.2.2 Bernoulli-Euler Beam

7.3 Hamilton's Principle for Piezoelectricity

7.3.1 Uniaxial Rod

7.3.2 Bernoulli-Euler Beam

7.4 Bernoulli-Euler Beam with a Shunt Circuit

7.5 Relationship to other Variational Principles

7.6 Lagrangian Densities

7.7 Problems

Chapter 8 Approximations

8.1 Classical, Strong, and Weak Formulations

8.1.1 Classical Solutions

8.1.2 Strong and Weak Solutions

8.2 Modeling Damping and Dissipation

8.3 Galerkin Approximations

8.3.1 Modal or Eigenfunction Approximations

8.3.2 Finite Element Approximations

8.4 Problems

Supplementary Material

Bibliography

Index

EULA.

Notes:

Description based on print version record.

ISBN:

9781523154951

1523154950

9781119393528

1119393523

9781119393382

1119393388

9781119393504

1119393507

OCLC:

1251440877